Logic grids

Hello, and welcome to Myriora Maths! Amy, Ben and Cara each have one pet: a cat, a dog or a fish. Ben has the fish. Amy doesn't have the dog. Who has which pet?

Logic puzzles are easy with a grid. Put the children down the side, and the pets along the top. Each child has exactly one pet, so each row will have one tick. And each pet belongs to one child, so each column will have one tick.

Clue one: Ben has the fish. Tick it. Now nobody else can have the fish, so cross out the rest of that column. And Ben can't have another pet, so cross out the rest of his row.

Clue two: Amy doesn't have the dog. Put a cross there.

Now look at Amy's row. The fish and the dog are crossed out, so Amy must have the cat! Tick it, and cross out the cat for Cara. That leaves Cara with the dog.

Why does the grid work? Every tick lets you cross out a whole row and a whole column. And when only one box is left in a row or a column, it must be a tick.

A common mistake is guessing too early. After the second clue, some people say Amy must have the fish. But Ben already has the fish! Use every clue, and let the grid tell you: Amy has the cat.

Your turn! Dan, Eve and Fay each play one sport: football, swimming or tennis. Eve doesn't play tennis. Fay doesn't play football or tennis. Who plays which sport? You've got twenty seconds, or pause the video if you need more time. Go!

Time's up! Fay doesn't play football or tennis, so Fay swims. Eve doesn't play tennis, and swimming is taken, so Eve plays football. That leaves tennis for Dan!

Quick review. Draw a grid, with one tick in every row and every column. Each tick crosses out the rest of its row and column. When only one box is left, it must be a tick. See you next time!